On hints sheet, This has 3 parts. Justify your answer to last part w/ a proof or counterexample.

Thank you

For Part 1: Suppose f is not injective. Then there exist such that a is not equal to b and . By definition, and . But in order for g to be a function, , which is a contradiction.

Apr 29th 2008, 07:50 PM

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Quote:

Originally Posted by icemanfan

For Part 1: Suppose f is not injective. Then there exist such that a is not equal to b and . By definition, and . But in order for g to be a function, , which is a contradiction.

Thank you for your help.
Can I prvoe g's being surjective by same way?
Like,

Suppose g is not surjective. Then there exists such that a is not contained in the image of set Y. By definition, g(a) doesn't exist. But in order for g to be a function, g(a) should be defined(not sure about this part).